Finite Group Databasebeta

← #29646471

Subgroups — #29646471

Order 15616.

1292 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#41×D61C211yesmaximal, characteristic
2#21454450C211yesmaximal, characteristic, complemented
3#423×D61C211yesmaximal, characteristic, complemented
4#21444259C211yesmaximal, characteristic, complemented
5#21444258C211yesmaximal, characteristic, complemented
6#21444256C211yesmaximal, characteristic, complemented
7#21444246C212yesmaximal, complemented
8#21444242C212yesmaximal, complemented
9#21444205C212yesmaximal, complemented
10#21444203C212yesmaximal, complemented
11C61×#1489C211yesmaximal, characteristic, complemented
12C2×#41×D61C411yescharacteristic
13C2×M16×D61—21no—
14#41×Dic61C411yescharacteristic
15C4×#11758226C411yescharacteristic
16C4×#11758226C2211yescharacteristic
17C4×#11758222—21no—
18C4×#11758222C2211yescharacteristic
19#16840230—21no—
20#16840230C411yescharacteristic
21C4×#11758224—21no—
22C4×#11758224—21no—
23C4×#11758224C411yescharacteristic
24C4×#11758224C2211yescharacteristic
25C4×Q8×D61C411yescharacteristic
26C4×Q8×D61C2211yescharacteristic
27C4×D4×D61—21no—
28C4×D4×D61—21no—
29C4×D4×D61C411yescharacteristic
30C4×D4×D61C2211yescharacteristic
31#117×D61—21no—
32#117×D61C411yescharacteristic
33C2×C42×D61—21no—
34C2×C42×D61C2211yescharacteristic
35#16839817—21no—
36#16839817—21no—
37#16839813C2212yes—
38#16839813C2212yescomplemented
39#16839786C2211yescharacteristic, complemented
40#16839785—21no—
41#16839785—21no—
42#16839784—21no—
43#16839784C2212yes—
44C4⋊C8×D61—21no—
45C4⋊C8×D61C2212yescomplemented
46#16839725—21no—
47C4×#11758194C2211yescharacteristic, complemented
48#16839494C2212yescomplemented
49Q8⋊#92418C2212yescomplemented
50#16839492C2212yescomplemented
51#16839491C2212yescomplemented
52D4⋊#92418C2212yescomplemented
53#16839489C2212yescomplemented
54C4×#41×C61C2211yescharacteristic
55C61×#423C2211yescharacteristic, complemented
56C4×M16×C61C2211yescharacteristic, complemented
57C61×Q8⋊C8C2212yescomplemented
58C61×D4⋊C8C2212yescomplemented
59C2×#11758226C2×C411yescharacteristic
60C2×#11758222—21no—
61C2×#11758222C2×C411yescharacteristic
62C2×#11758224—21no—
63C2×#11758224C2×C411yescharacteristic
64#41×D61—24no—
65#41×D61—24no—
66C2×Q8×D61C2×C411yescharacteristic
67C2×D4×D61—21no—
68C2×D4×D61C2×C411yescharacteristic
69C22×C4×D61—21no—
70C22×C4×D61—21no—
71C22×C4×D61—21no—
72C22×C4×D61C2×C411yescharacteristic
73C22×C4×D61D411yescharacteristic
74C22×C4×D61D411yescharacteristic
75C2×#11758194—21no—
76C2×#11758194—21no—
77C2×#11758189—22no—
78M16×D61—44no—
79C2×C8×D61—22no—
80Q8×Dic61C2×C411yescharacteristic
81Q8×Dic61C2×C411yescharacteristic
82C4×Dic122—21no—
83C4×Dic122—21no—
84C4×Dic122C2×C411yescharacteristic
85C4×Dic122C2311yescharacteristic
86#14519742—21no—
87#14519742—21no—
88#14519742C2×C411yescharacteristic
89#14519742C2×C411yescharacteristic
90C4×D244—21no—
91C4×D244—21no—
92C4×D244C2×C411yescharacteristic
93C4×D244C2311yescharacteristic
94D4×Dic61—21no—
95D4×Dic61—21no—
96D4×Dic61C2×C411yescharacteristic
97D4×Dic61C2×C411yescharacteristic
98#14519739—21no—
99#14519739—21no—
100#14519739C2×C411yescharacteristic
101#14519739C2×C411yescharacteristic
102C4×C22⋊D61—21no—
103C4×C22⋊D61—21no—
104C4×C22⋊D61—21no—
105C4×C22⋊D61—21no—
106C4×C22⋊D61—21no—
107C4×C22⋊D61—21no—
108#14519737—21no—
109#14519737—21no—
110#14519737—21no—
111#14519737—21no—
112#14519737—21no—
113#14519737—21no—
114#14519736—21no—
115#14519736C2×C411yescharacteristic
116#14519735—21no—
117#14519735—21no—
118#14519735C2×C411yescharacteristic
119#14519735C2×C411yescharacteristic
120#14519734—21no—
121#14519734—21no—
122#14519734—21no—
123#14519733—21no—
124#14519733—21no—
125#14519733—21no—
126C4⋊C4×D61—21no—
127C4⋊C4×D61—21no—
128C4⋊C4×D61C2×C411yescharacteristic
129C4⋊C4×D61C2×C411yescharacteristic
130C22⋊C4×D61—21no—
131C22⋊C4×D61—21no—
132C22⋊C4×D61—21no—
133C2×C4×Dic61—21no—
134C2×C4×Dic61—21no—
135C2×C4×Dic61—21no—
136C2×C4×Dic61C2×C411yescharacteristic
137C2×C4×Dic61D411yescharacteristic
138C2×C4×Dic61D411yescharacteristic
139C42×D61—21no—
140C42×D61—21no—
141C42×D61—21no—
142C42×D61—21no—
143C42×D61—21no—
144C42×D61—21no—
145C42×D61—21no—
146C42×D61C2×C411yescharacteristic
147C42×D61C2×C411yescharacteristic
148C42×D61D411yescharacteristic
149C42×D61D411yescharacteristic
150C42×D61D411yescharacteristic
151C42×D61D411yescharacteristic
152C42×D61C2311yescharacteristic
153C42×D61C2311yescharacteristic
154C4⋊#92418—21no—
155C4⋊#92418C2312yes—
156#14519706—22no—
157#14519706—22no—
158#14519706—22no—
159#14519706—22no—
160#14519689—22no—
161#14519689—22no—
162#14519688—21no—
163C4×#92418C2312yes—
164C2×#41×C61C2×C411yescharacteristic
165C2×M16×C61—21no—
166C2×M16×C61—21no—
167C4×Q8×C61C2×C411yescharacteristic
168C4×Q8×C61C2311yescharacteristic
169C4×D4×C61—21no—
170C4×D4×C61—21no—
171C4×D4×C61C2×C411yescharacteristic
172C4×D4×C61C2311yescharacteristic
173#117×C61—21no—
174#117×C61C2×C411yescharacteristic
175C2×C42×C61—21no—
176C2×C42×C61C2311yescharacteristic
177C4⋊C8×C61—21no—
178C4⋊C8×C61C2312yes—
179#97×C61—21no—
180C4×C8×C61C2312yes—
181C23×D61—21no—
182C23×D61C22⋊C411yescharacteristic
183#41×C61—22no—
184#41×C61—22no—
185C2×Q8×C61C22×C411yescharacteristic
186C2×D4×C61—21no—
187C2×D4×C61C22×C411yescharacteristic
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61C22×C411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2×D411yescharacteristic
194C2×C22⋊D61—21no—
195C2×C22⋊D61—21no—
196C2×C22⋊D61—21no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61C22⋊C411yescharacteristic
201C22×Dic61C22⋊C411yescharacteristic
202C22×Dic61C22⋊C411yescharacteristic
203#11758226—22no—
204#11758226M1614yescomplemented
205Q8×D61—22no—
206Q8×D61—22no—
207#11758224—28no—
208#11758224—22no—
209#11758224M1614yescomplemented
210D4×D61—28no—
211D4×D61—22no—
212D4×D61—22no—
213#11758222—28no—
214#11758222—22no—
215#11758222—22no—
216C2×D244—21no—
217C2×D244C22×C411yescharacteristic
218C2×C4×D61—28no—
219C2×C4×D61—21no—
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61—22no—
223C2×C4×D61—22no—
224C2×C4×D61—22no—
225C2×C4×D61—22no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—42no—
233C2×C4×D61—44no—
234C2×C4×D61—42no—
235C2×C4×D61—42no—
236C2×C4×D61C22⋊C411yescharacteristic
237C2×C4×D61C22⋊C411yescharacteristic
238C2×C4×D61C22⋊C411yescharacteristic
239C2×C4×D61C22⋊C411yescharacteristic
240C2×C4×D61C22⋊C411yescharacteristic
241C2×C4×D61C22⋊C411yescharacteristic
242C2×C4×D61C22×C411yescharacteristic
243C2×C4×D61C22×C411yescharacteristic
244C2×C4×D61C2×D411yescharacteristic
245C2×C4×D61C2×D411yescharacteristic
246C2×C4×D61C2×D411yescharacteristic
247C2×C4×D61C2×D411yescharacteristic
248C2×Dic122—21no—
249C2×Dic122C22×C411yescharacteristic
250M16×C61—42no—
251M16×C61—42no—
252C2×C8×C61—22no—
253C2×C8×C61—22no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61C22×C411yescharacteristic
257C4⋊C4×C61C22×C411yescharacteristic
258C22⋊C4×C61—21no—
259C22⋊C4×C61—21no—
260C22⋊C4×C61—21no—
261C42×C61—21no—
262C42×C61—21no—
263C42×C61—21no—
264C42×C61C22×C411yescharacteristic
265C42×C61C2×D411yescharacteristic
266C42×C61C2×D411yescharacteristic
267C42×C61C2411yescharacteristic
268C22⋊Dic61—21no—
269C22⋊Dic61—21no—
270C22⋊Dic61—21no—
271#11758198—21no—
272#11758198—21no—
273#11758198—21no—
274#11758198—21no—
275#11758198—21no—
276#11758198—21no—
277C4⋊Dic61—21no—
278C4⋊Dic61—21no—
279C4⋊Dic61C22×C411yescharacteristic
280C4⋊Dic61C22×C411yescharacteristic
281#11758196—21no—
282#11758196—21no—
283#11758196—21no—
284#11758196—21no—
285#11758196—21no—
286#11758196—21no—
287C4×Dic61—21no—
288C4×Dic61—21no—
289C4×Dic61—21no—
290C4×Dic61—21no—
291C4×Dic61—21no—
292C4×Dic61—21no—
293C4×Dic61—21no—
294C4×Dic61—21no—
295C4×Dic61—21no—
296C4×Dic61C22⋊C411yescharacteristic
297C4×Dic61C22⋊C411yescharacteristic
298C4×Dic61C22⋊C411yescharacteristic
299C4×Dic61C22⋊C411yescharacteristic
300C4×Dic61C22⋊C411yescharacteristic
301C4×Dic61C22⋊C411yescharacteristic
302C4×Dic61C22×C411yescharacteristic
303C4×Dic61C22×C411yescharacteristic
304C4×Dic61C2×D411yescharacteristic
305C4×Dic61C2×D411yescharacteristic
306C4×Dic61C2×D411yescharacteristic
307C4×Dic61C2×D411yescharacteristic
308#11758194—42no—
309#11758194—42no—
310C2×#92418—22no—
311C2×#92418—22no—
312#11758189—44no—
313C8×D61—44no—
314C23×C61—21no—
315C23×C61C2×C22⋊C411yescharacteristic
316C22×D61—24no—
317C22×D61—21no—
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—41no—
321C22×D61—42no—
322C22×D61—42no—
323C22×D61C2×C22⋊C411yescharacteristic
324C22×D61C2×C22⋊C411yescharacteristic
325Q8×C61—21no—
326Q8×C61C2×M1612yescomplemented
327D4×C61—24no—
328D4×C61—21no—
329D4×C61C2×M1612yescomplemented
330C2×C4×C61—24no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—22no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—42no—
342C2×C4×C61C2×C22⋊C411yescharacteristic
343C2×C4×C61C2×C22⋊C411yescharacteristic
344C2×C4×C61C2×C22⋊C411yescharacteristic
345C2×C4×C61C23×C411yescharacteristic
346C2×C4×C61C22×D411yescharacteristic
347C2×C4×C61C22×D411yescharacteristic
348C22⋊D61—24no—
349C22⋊D61—24no—
350C22⋊D61—24no—
351C2×Dic61—21no—
352C2×Dic61—22no—
353C2×Dic61—24no—
354C2×Dic61—22no—
355C2×Dic61—21no—
356C2×Dic61—21no—
357C2×Dic61—41no—
358C2×Dic61—42no—
359C2×Dic61—42no—
360C2×Dic61C2×C22⋊C411yescharacteristic
361C2×Dic61C2×C22⋊C411yescharacteristic
362C2×Dic61C2×C22⋊C411yescharacteristic
363C2×Dic61C2×C22⋊C411yescharacteristic
364C2×Dic61C2×C22⋊C411yescharacteristic
365C2×Dic61C2×C22⋊C411yescharacteristic
366D244—24no—
367D244—21no—
368D244C2×M1612yescomplemented
369C4×D61—24no—
370C4×D61—24no—
371C4×D61—22no—
372C4×D61—22no—
373C4×D61—21no—
374C4×D61—21no—
375C4×D61—21no—
376C4×D61—21no—
377C4×D61—22no—
378C4×D61—22no—
379C4×D61—22no—
380C4×D61—24no—
381C4×D61—22no—
382C4×D61—41no—
383C4×D61—41no—
384C4×D61—42no—
385C4×D61—42no—
386C4×D61—42no—
387C4×D61—41no—
388C4×D61—41no—
389C4×D61—42no—
390C4×D61—42no—
391C4×D61C2×M1612yes—
392C4×D61C2×M1612yes—
393C4×D61AGL(1,ℤ/8)12yes—
394C4×D61#13712yes—
395Dic122—24no—
396Dic122—21no—
397Dic122C2×M1612yescomplemented
398C8×C61—42no—
399C8×C61—42no—
400#92418—42no—
401#92418—42no—
402#17451—611nomaximal, Sylow
403C22×C61—21no—
404C22×C61—22no—
405C22×C61—21no—
406C22×C61—21no—
407C22×C61—41no—
408C22×C61—41no—
409C22×C61C22×C22⋊C411yescharacteristic
410C2×D61—21no—
411C2×D61—21no—
412C2×D61—21no—
413C2×D61—21no—
414C2×D61—22no—
415C2×D61—44no—
416C2×D61—48no—
417C2×D61—41no—
418C2×D61—41no—
419C2×D61#40712yes—
420C2×D61#41712yes—
421C4×C61—22no—
422C4×C61—21no—
423C4×C61—21no—
424C4×C61—21no—
425C4×C61—41no—
426C4×C61—41no—
427C4×C61#42112yes—
428C4×C61C22×M1611yescharacteristic
429C4×C61C22×M1611yescharacteristic
430C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
431C4×C61C2×#13711yescharacteristic
432Dic61—21no—
433Dic61—22no—
434Dic61—21no—
435Dic61—21no—
436Dic61—21no—
437Dic61—41no—
438Dic61—41no—
439Dic61#40712yes—
440Dic61#41712yes—
441C2×C4×#41—611no—
442#2920—611no—
443C2×#423—611no—
444#1489—611no—
445#1489—611no—
446#1489—611no—
447#1489D6111yescharacteristic, complemented
448#1487—612no—
449#1486—612no—
450#1477—612no—
451#1477—612no—
452C2×C61—41no—
453C2×C61—42no—
454C2×C61C2×#40711yescharacteristic
455C2×C61C2×#41711yescharacteristic
456C2×C61C2×#42111yescharacteristic
457D61—22no—
458D61—22no—
459D61—42no—
460C22×#41—611no—
461C22×M16—1221no—
462C4×#41—611no—
463C4×#41—611no—
464C4×#41—611no—
465C4×#41—611no—
466C4×#41—611no—
467C4×#41—611no—
468C4×#41—611no—
469C4×#41—1221no—
470C4×#41—1221no—
471C4×#41—1221no—
472C4×#41—1221no—
473C4×#41C2×D6111yescharacteristic
474C2×C4×Q8—611no—
475C2×C4×Q8—611no—
476C2×C4×D4—611no—
477C2×C4×D4—611no—
478C2×C4×D4—1221no—
479C2×C4×D4—1221no—
480C2×#117—611no—
481C2×#117—1221no—
482C22×C42—611no—
483C22×C42—1221no—
484#432—1221no—
485#432—1221no—
486#431—612no—
487#431—612no—
488#423—611no—
489#423—612no—
490#423—1221no—
491#423—1221no—
492#423—1221no—
493#423C2×D6111yescharacteristic, complemented
494C2×C4⋊C8—612no—
495C2×C4⋊C8—1221no—
496#407—1221no—
497C4×M16—611no—
498C4×M16C2×D6111yescharacteristic, complemented
499Q8⋊C8—612no—
500Q8⋊C8—612no—
501Q8⋊C8—612no—
502Q8⋊C8C2×D6112yescomplemented
503D4⋊C8—612no—
504D4⋊C8—612no—
505D4⋊C8—612no—
506D4⋊C8C2×D6112yescomplemented
507C61#1745111yescharacteristic, complemented, Sylow
508C2×#41—611no—
509C2×#41—611no—
510C2×#41—611no—
511C2×#41—1221no—
512C2×#41—1221no—
513C2×#41—1224no—
514C2×#41—1224no—
515C2×#41C4×D6111yescharacteristic
516C22×Q8—611no—
517C22×D4—611no—
518C22×D4—1221no—
519C23×C4—611no—
520C23×C4—611no—
521C23×C4—611no—
522C23×C4—1221no—
523C23×C4—1221no—
524C23×C4—1221no—
525C2×M16—21no—
526C2×M16—21no—
527C2×M16—1222no—
528C2×M16—1221no—
529C2×M16—1221no—
530C2×M16—2444no—
531C22×C8—1222no—
532C4×Q8—611no—
533C4×Q8—611no—
534C4×Q8—611no—
535C4×Q8—611no—
536C4×Q8—611no—
537C4×Q8—611no—
538C4×Q8—1221no—
539C4×Q8—1221no—
540C4×Q8—1221no—
541C4×Q8—1221no—
542C4×Q8C4×D6111yescharacteristic
543C4×Q8C22×D6111yescharacteristic
544C4×D4—21no—
545C4×D4—21no—
546C4×D4—611no—
547C4×D4—611no—
548C4×D4—611no—
549C4×D4—611no—
550C4×D4—611no—
551C4×D4—611no—
552C4×D4—1221no—
553C4×D4—1221no—
554C4×D4—1221no—
555C4×D4—1221no—
556C4×D4—1221no—
557C4×D4—1221no—
558C4×D4—1221no—
559C4×D4—1221no—
560C4×D4—1221no—
561C4×D4—1221no—
562C4×D4—1221no—
563C4×D4—1221no—
564C4×D4—1221no—
565C4×D4—1221no—
566C4×D4—1221no—
567C4×D4—1221no—
568C4×D4—1221no—
569C4×D4—1221no—
570C4×D4C4×D6111yescharacteristic
571C4×D4C22×D6111yescharacteristic
572#117—21no—
573#117—611no—
574#117—611no—
575#117—611no—
576#117—1221no—
577#117—1221no—
578#117—1221no—
579#117—1221no—
580#117—1221no—
581#117—1221no—
582#117—1221no—
583#117—1221no—
584#117—1221no—
585#117C4×D6111yescharacteristic
586C2×C4⋊C4—611no—
587C2×C4⋊C4—611no—
588C2×C4⋊C4—1221no—
589C2×C4⋊C4—1221no—
590C2×C22⋊C4—1221no—
591C2×C22⋊C4—1221no—
592C2×C22⋊C4—1221no—
593C2×C42—21no—
594C2×C42—611no—
595C2×C42—611no—
596C2×C42—611no—
597C2×C42—611no—
598C2×C42—611no—
599C2×C42—611no—
600C2×C42—611no—
601C2×C42—611no—
602C2×C42—611no—
603C2×C42—611no—
604C2×C42—611no—
605C2×C42—1221no—
606C2×C42—1221no—
607C2×C42—1221no—
608C2×C42—1221no—
609C2×C42—1221no—
610C2×C42—1221no—
611C2×C42—1221no—
612C2×C42—1221no—
613C2×C42—1221no—
614C2×C42—1221no—
615C2×C42C22×D6111yescharacteristic
616C4⋊C8—21no—
617C4⋊C8—612no—
618C4⋊C8—1222no—
619C4⋊C8—1222no—
620C4⋊C8—1222no—
621C4⋊C8—1222no—
622C4⋊C8—1221no—
623C4⋊C8C22×D6112yes—
624C22⋊C8—1222no—
625C22⋊C8—1222no—
626#97—21no—
627#97—1221no—
628C4×C8—612no—
629C4×C8C22×D6112yes—
630C24—611no—
631C24—1221no—
632#41—22no—
633#41—22no—
634#41—614no—
635#41—614no—
636#41—1222no—
637#41—1222no—
638#41—1228no—
639#41—1222no—
640#41—1222no—
641#41—1228no—
642C2×Q8—611no—
643C2×Q8—1221no—
644C2×Q8—1222no—
645C2×Q8—1222no—
646C2×Q8C2×C4×D6111yescharacteristic
647C2×D4—21no—
648C2×D4—611no—
649C2×D4—1221no—
650C2×D4—1221no—
651C2×D4—1222no—
652C2×D4—1228no—
653C2×D4—1221no—
654C2×D4—1221no—
655C2×D4—1222no—
656C2×D4C2×C4×D6111yescharacteristic
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—611no—
661C22×C4—611no—
662C22×C4—611no—
663C22×C4—611no—
664C22×C4—611no—
665C22×C4—611no—
666C22×C4—611no—
667C22×C4—611no—
668C22×C4—611no—
669C22×C4—611no—
670C22×C4—611no—
671C22×C4—611no—
672C22×C4—611no—
673C22×C4—611no—
674C22×C4—611no—
675C22×C4—1221no—
676C22×C4—1222no—
677C22×C4—1222no—
678C22×C4—1222no—
679C22×C4—1222no—
680C22×C4—1221no—
681C22×C4—1221no—
682C22×C4—1221no—
683C22×C4—1228no—
684C22×C4—1221no—
685C22×C4—1221no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4—1221no—
689C22×C4—1221no—
690C22×C4—1221no—
691C22×C4—1221no—
692C22×C4—2442no—
693C22×C4—2442no—
694C22×C4—2442no—
695C22×C4—2444no—
696C22×C4C2×C4×D6111yescharacteristic
697C22×C4D4×D6111yescharacteristic
698C22×C4D4×D6111yescharacteristic
699M16—42no—
700M16—42no—
701M16—2444no—
702M16—2442no—
703M16—2442no—
704C2×C8—22no—
705C2×C8—22no—
706C2×C8—1222no—
707C2×C8—1222no—
708C2×C8—2444no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—611no—
712C4⋊C4—611no—
713C4⋊C4—1221no—
714C4⋊C4—1221no—
715C4⋊C4—1221no—
716C4⋊C4—1221no—
717C4⋊C4—1221no—
718C4⋊C4—1221no—
719C4⋊C4—1221no—
720C4⋊C4—1221no—
721C4⋊C4C2×C4×D6111yescharacteristic
722C4⋊C4C2×C4×D6111yescharacteristic
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—1221no—
727C22⋊C4—1221no—
728C22⋊C4—1221no—
729C22⋊C4—1221no—
730C22⋊C4—1221no—
731C22⋊C4—1221no—
732C22⋊C4—1221no—
733C22⋊C4—1221no—
734C22⋊C4—1221no—
735C42—21no—
736C42—21no—
737C42—21no—
738C42—611no—
739C42—611no—
740C42—611no—
741C42—611no—
742C42—611no—
743C42—611no—
744C42—611no—
745C42—611no—
746C42—611no—
747C42—611no—
748C42—611no—
749C42—611no—
750C42—1221no—
751C42—1221no—
752C42—1221no—
753C42—1221no—
754C42—1221no—
755C42—1221no—
756C42—1221no—
757C42—1221no—
758C42—1221no—
759C42C2×C4×D6111yescharacteristic
760C42D4×D6111yescharacteristic
761C42D4×D6111yescharacteristic
762C42C23×D6111yescharacteristic
763C23—21no—
764C23—611no—
765C23—611no—
766C23—1222no—
767C23—1222no—
768C23—1224no—
769C23—1221no—
770C23—2441no—
771C23—2442no—
772C23—2442no—
773C23C22⋊C4×D6111yescharacteristic
774Q8—21no—
775Q8—612no—
776Q8—1224no—
777Q8—1221no—
778Q8M16×D6112yescomplemented
779D4—24no—
780D4—21no—
781D4—612no—
782D4—1224no—
783D4—1224no—
784D4—1224no—
785D4—1224no—
786D4—1221no—
787D4M16×D6112yescomplemented
788C2×C4—24no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—611no—
801C2×C4—611no—
802C2×C4—612no—
803C2×C4—612no—
804C2×C4—612no—
805C2×C4—612no—
806C2×C4—611no—
807C2×C4—611no—
808C2×C4—611no—
809C2×C4—611no—
810C2×C4—1222no—
811C2×C4—1222no—
812C2×C4—1224no—
813C2×C4—1222no—
814C2×C4—1222no—
815C2×C4—1224no—
816C2×C4—1224no—
817C2×C4—1222no—
818C2×C4—1222no—
819C2×C4—1224no—
820C2×C4—1221no—
821C2×C4—1221no—
822C2×C4—1221no—
823C2×C4—1222no—
824C2×C4—1222no—
825C2×C4—1221no—
826C2×C4—1221no—
827C2×C4—1221no—
828C2×C4—1221no—
829C2×C4—2441no—
830C2×C4—2441no—
831C2×C4—2442no—
832C2×C4—2442no—
833C2×C4—2442no—
834C2×C4—2442no—
835C2×C4—2442no—
836C2×C4—2441no—
837C2×C4—2442no—
838C2×C4—2442no—
839C2×C4—2441no—
840C2×C4—2441no—
841C2×C4C22⋊C4×D6111yescharacteristic
842C2×C4C22⋊C4×D6111yescharacteristic
843C2×C4C22⋊C4×D6111yescharacteristic
844C2×C4C22×C4×D6111yescharacteristic
845C2×C4C2×D4×D6111yescharacteristic
846C2×C4C2×D4×D6111yescharacteristic
847C8—42no—
848C8—42no—
849C8—2442no—
850C8—2442no—
851C22—21no—
852C22—21no—
853C22—22no—
854C22—21no—
855C22—41no—
856C22—41no—
857C22—612no—
858C22—612no—
859C22—1221no—
860C22—1221no—
861C22—1221no—
862C22—1221no—
863C22—1222no—
864C22—2444no—
865C22—2448no—
866C22—2441no—
867C22—2441no—
868C22C2×C22⋊C4×D6111yescharacteristic
869C4—21no—
870C4—21no—
871C4—22no—
872C4—21no—
873C4—41no—
874C4—41no—
875C4—612no—
876C4—612no—
877C4—1221no—
878C4—1221no—
879C4—1221no—
880C4—1222no—
881C4—1221no—
882C4—2441no—
883C4—2441no—
884C4#1683977712yes—
885C4C2×M16×D6111yescharacteristic
886C4C2×M16×D6111yescharacteristic
887C4AGL(1,ℤ/8)×D6111yescharacteristic
888C4#137×D6111yescharacteristic
889C2—41no—
890C2—42no—
891C2—1222no—
892C2—1222no—
893C2—2442no—
894C2#407×D6111yescharacteristic
895C2#417×D6111yescharacteristic
896C2C2×#1683977711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1489C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#41×D61C4
cosocleC42×C61C24
hypercenter#1489D61
hypocenterC61#17451
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1489

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #21454450C2semidirect
3. #423×D61C2semidirect
4. #21444259C2semidirect
5. #21444258C2semidirect
6. #21444256C2semidirect
7. #21444246C2semidirect
8. #21444242C2semidirect
9. #21444205C2semidirect
10. #21444203C2semidirect
11. C61×#1489C2semidirect
38. #16839813C22semidirect
39. #16839786C22semidirect
45. C4⋊C8×D61C22semidirect
47. C4×#11758194C22semidirect
48. #16839494C22semidirect
49. Q8⋊#92418C22semidirect
50. #16839492C22semidirect
51. #16839491C22semidirect
52. D4⋊#92418C22semidirect
53. #16839489C22semidirect
55. C61×#423C22semidirect
56. C4×M16×C61C22semidirect
57. C61×Q8⋊C8C22semidirect
58. C61×D4⋊C8C22semidirect
204. #11758226M16semidirect
209. #11758224M16semidirect
326. Q8×C61C2×M16semidirect
329. D4×C61C2×M16semidirect
368. D244C2×M16semidirect
397. Dic122C2×M16semidirect
447. #1489D61semidirect
493. #423C2×D61semidirect
498. C4×M16C2×D61semidirect
502. Q8⋊C8C2×D61semidirect
506. D4⋊C8C2×D61semidirect
507. C61#17451semidirect
778. Q8M16×D61semidirect
787. D4M16×D61semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C4×#41×D612
#214544502
#423×D612
#214442592
#214442582
#214442562
#214442462
#214442422
#214442052
#214442032
C61×#14892
#1745161